Is the BBS saying that the Sun’s output is increasing? I have never hear that one before. If that happened, Mars, Ceres, Callisto, Ganamede, and Titan might become very pleasant places to live.
No, they are saying that the sun is expanding as part of the normal life cycle of a star and as it does we will get warmer and eventually be destroyed. Astronaut Mike Massimo did a documentary on it Video here it's watchable but don't click on the link as they suggest. Since you live in the USA (I live in Spain) you may find it on one of the streaming TV services in better quality.